Saturday, December 12, 2009

Bertrand's Paradox

This paradox was discovered by Bertrand Russell in 1901.

Some classes are members of themselves; some are not. For example, the class of all classes that have more than five members clearly has more than five classes as members; therefore the class is a member of itself. On the other hand, the class of all men is not a member of itself, not being a man. What of the class of all classes that are not members of themselves? Since its members are the non-self-members, it qualifies as a member of itself if and only if it is not.

Friday, December 11, 2009

It Begins

Okay so I have been thinking lately that I want a place where I can write about what I think about. A place where people can respond or share their opinions on the topics I present. I will probably just respond to things I read, at least at the beginning, because lately I have noticed that all these great things I read are very difficult to remember a few months later and I want to be able to look back at this and remember the ideas and topics that I felt were noteworthy. Other than that I hope to have the presence of mind to retain the ideas as I read them so that they actually make it to this blog. And excuse me if I happen to make a few random posts here and there.

"A mind always employed is always happy."